Properties

Label 729.2.g.c.676.3
Level $729$
Weight $2$
Character 729.676
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(28,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([44]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.g (of order \(27\), degree \(18\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 676.3
Character \(\chi\) \(=\) 729.676
Dual form 729.2.g.c.55.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.588281 - 1.36379i) q^{2} +(-0.141360 + 0.149832i) q^{4} +(-0.0932044 + 1.60026i) q^{5} +(-1.85061 + 0.438602i) q^{7} +(-2.50387 - 0.911335i) q^{8} +O(q^{10})\) \(q+(-0.588281 - 1.36379i) q^{2} +(-0.141360 + 0.149832i) q^{4} +(-0.0932044 + 1.60026i) q^{5} +(-1.85061 + 0.438602i) q^{7} +(-2.50387 - 0.911335i) q^{8} +(2.23724 - 0.814290i) q^{10} +(-3.38752 + 2.22800i) q^{11} +(1.67851 - 0.196189i) q^{13} +(1.68684 + 2.26582i) q^{14} +(0.254067 + 4.36216i) q^{16} +(4.14727 + 3.47997i) q^{17} +(3.70167 - 3.10607i) q^{19} +(-0.226595 - 0.240177i) q^{20} +(5.03133 + 3.30916i) q^{22} +(0.651612 + 0.154435i) q^{23} +(2.41405 + 0.282162i) q^{25} +(-1.25499 - 2.17371i) q^{26} +(0.195884 - 0.339282i) q^{28} +(-2.85835 + 3.83943i) q^{29} +(1.39576 + 4.66216i) q^{31} +(1.03731 - 0.520955i) q^{32} +(2.30618 - 7.70319i) q^{34} +(-0.529392 - 3.00233i) q^{35} +(-2.07926 + 11.7921i) q^{37} +(-6.41363 - 3.22105i) q^{38} +(1.69174 - 3.92190i) q^{40} +(-4.00621 + 9.28743i) q^{41} +(7.64192 + 3.83792i) q^{43} +(0.145031 - 0.822509i) q^{44} +(-0.172714 - 0.979511i) q^{46} +(0.0578400 - 0.193199i) q^{47} +(-3.02305 + 1.51823i) q^{49} +(-1.03533 - 3.45825i) q^{50} +(-0.207877 + 0.279228i) q^{52} +(2.48138 - 4.29788i) q^{53} +(-3.24965 - 5.62856i) q^{55} +(5.03340 + 0.588321i) q^{56} +(6.91768 + 1.63952i) q^{58} +(1.58520 + 1.04260i) q^{59} +(0.124028 + 0.131462i) q^{61} +(5.53710 - 4.64618i) q^{62} +(5.37384 + 4.50919i) q^{64} +(0.157509 + 2.70433i) q^{65} +(-7.95826 - 10.6898i) q^{67} +(-1.10767 + 0.129468i) q^{68} +(-3.78311 + 2.48819i) q^{70} +(9.41216 - 3.42575i) q^{71} +(-10.9327 - 3.97917i) q^{73} +(17.3051 - 4.10138i) q^{74} +(-0.0578765 + 0.993701i) q^{76} +(5.29176 - 5.60894i) q^{77} +(-1.45390 - 3.37053i) q^{79} -7.00426 q^{80} +15.0229 q^{82} +(-2.17367 - 5.03914i) q^{83} +(-5.95539 + 6.31235i) q^{85} +(0.738510 - 12.6797i) q^{86} +(10.5124 - 2.49148i) q^{88} +(-6.65218 - 2.42120i) q^{89} +(-3.02021 + 1.09927i) q^{91} +(-0.115251 + 0.0758017i) q^{92} +(-0.297508 + 0.0347738i) q^{94} +(4.62550 + 6.21312i) q^{95} +(0.0778051 + 1.33586i) q^{97} +(3.84894 + 3.22965i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8} - 18 q^{10} + 9 q^{11} + 9 q^{13} + 9 q^{14} + 9 q^{16} - 18 q^{17} - 18 q^{19} - 63 q^{20} + 9 q^{22} + 36 q^{23} + 9 q^{25} + 45 q^{26} - 9 q^{28} - 45 q^{29} + 9 q^{31} + 63 q^{32} + 9 q^{34} + 9 q^{35} - 18 q^{37} - 9 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} + 54 q^{44} - 18 q^{46} + 63 q^{47} + 9 q^{49} - 225 q^{50} + 27 q^{52} + 45 q^{53} - 9 q^{55} + 99 q^{56} + 9 q^{58} - 117 q^{59} + 9 q^{61} + 81 q^{62} - 18 q^{64} + 81 q^{65} + 36 q^{67} - 18 q^{68} + 63 q^{70} - 90 q^{71} - 18 q^{73} + 81 q^{74} + 90 q^{76} + 81 q^{77} + 63 q^{79} - 288 q^{80} - 36 q^{82} + 45 q^{83} + 63 q^{85} + 81 q^{86} + 90 q^{88} - 81 q^{89} - 18 q^{91} - 63 q^{92} + 63 q^{94} + 153 q^{95} + 36 q^{97} + 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{10}{27}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.588281 1.36379i −0.415977 0.964344i −0.989418 0.145096i \(-0.953651\pi\)
0.573440 0.819247i \(-0.305608\pi\)
\(3\) 0 0
\(4\) −0.141360 + 0.149832i −0.0706798 + 0.0749162i
\(5\) −0.0932044 + 1.60026i −0.0416823 + 0.715657i 0.911134 + 0.412110i \(0.135208\pi\)
−0.952816 + 0.303547i \(0.901829\pi\)
\(6\) 0 0
\(7\) −1.85061 + 0.438602i −0.699465 + 0.165776i −0.564937 0.825134i \(-0.691100\pi\)
−0.134527 + 0.990910i \(0.542952\pi\)
\(8\) −2.50387 0.911335i −0.885253 0.322206i
\(9\) 0 0
\(10\) 2.23724 0.814290i 0.707478 0.257501i
\(11\) −3.38752 + 2.22800i −1.02137 + 0.671769i −0.945592 0.325356i \(-0.894516\pi\)
−0.0757828 + 0.997124i \(0.524146\pi\)
\(12\) 0 0
\(13\) 1.67851 0.196189i 0.465534 0.0544131i 0.119907 0.992785i \(-0.461740\pi\)
0.345627 + 0.938372i \(0.387666\pi\)
\(14\) 1.68684 + 2.26582i 0.450826 + 0.605565i
\(15\) 0 0
\(16\) 0.254067 + 4.36216i 0.0635167 + 1.09054i
\(17\) 4.14727 + 3.47997i 1.00586 + 0.844017i 0.987785 0.155820i \(-0.0498020\pi\)
0.0180743 + 0.999837i \(0.494246\pi\)
\(18\) 0 0
\(19\) 3.70167 3.10607i 0.849220 0.712581i −0.110397 0.993888i \(-0.535212\pi\)
0.959618 + 0.281307i \(0.0907679\pi\)
\(20\) −0.226595 0.240177i −0.0506682 0.0537052i
\(21\) 0 0
\(22\) 5.03133 + 3.30916i 1.07268 + 0.705515i
\(23\) 0.651612 + 0.154435i 0.135870 + 0.0322019i 0.297988 0.954570i \(-0.403684\pi\)
−0.162118 + 0.986771i \(0.551832\pi\)
\(24\) 0 0
\(25\) 2.41405 + 0.282162i 0.482811 + 0.0564325i
\(26\) −1.25499 2.17371i −0.246124 0.426300i
\(27\) 0 0
\(28\) 0.195884 0.339282i 0.0370187 0.0641182i
\(29\) −2.85835 + 3.83943i −0.530782 + 0.712965i −0.983947 0.178462i \(-0.942888\pi\)
0.453164 + 0.891427i \(0.350295\pi\)
\(30\) 0 0
\(31\) 1.39576 + 4.66216i 0.250686 + 0.837349i 0.987002 + 0.160711i \(0.0513786\pi\)
−0.736316 + 0.676638i \(0.763436\pi\)
\(32\) 1.03731 0.520955i 0.183372 0.0920927i
\(33\) 0 0
\(34\) 2.30618 7.70319i 0.395507 1.32109i
\(35\) −0.529392 3.00233i −0.0894836 0.507487i
\(36\) 0 0
\(37\) −2.07926 + 11.7921i −0.341829 + 1.93861i 0.00314382 + 0.999995i \(0.498999\pi\)
−0.344973 + 0.938613i \(0.612112\pi\)
\(38\) −6.41363 3.22105i −1.04043 0.522523i
\(39\) 0 0
\(40\) 1.69174 3.92190i 0.267488 0.620107i
\(41\) −4.00621 + 9.28743i −0.625664 + 1.45045i 0.250344 + 0.968157i \(0.419456\pi\)
−0.876009 + 0.482296i \(0.839803\pi\)
\(42\) 0 0
\(43\) 7.64192 + 3.83792i 1.16538 + 0.585277i 0.922961 0.384895i \(-0.125762\pi\)
0.242421 + 0.970171i \(0.422059\pi\)
\(44\) 0.145031 0.822509i 0.0218642 0.123998i
\(45\) 0 0
\(46\) −0.172714 0.979511i −0.0254653 0.144421i
\(47\) 0.0578400 0.193199i 0.00843683 0.0281810i −0.953667 0.300863i \(-0.902725\pi\)
0.962104 + 0.272682i \(0.0879106\pi\)
\(48\) 0 0
\(49\) −3.02305 + 1.51823i −0.431864 + 0.216890i
\(50\) −1.03533 3.45825i −0.146418 0.489070i
\(51\) 0 0
\(52\) −0.207877 + 0.279228i −0.0288274 + 0.0387219i
\(53\) 2.48138 4.29788i 0.340844 0.590359i −0.643746 0.765240i \(-0.722621\pi\)
0.984590 + 0.174880i \(0.0559538\pi\)
\(54\) 0 0
\(55\) −3.24965 5.62856i −0.438183 0.758955i
\(56\) 5.03340 + 0.588321i 0.672617 + 0.0786177i
\(57\) 0 0
\(58\) 6.91768 + 1.63952i 0.908336 + 0.215280i
\(59\) 1.58520 + 1.04260i 0.206375 + 0.135735i 0.648489 0.761224i \(-0.275401\pi\)
−0.442114 + 0.896959i \(0.645771\pi\)
\(60\) 0 0
\(61\) 0.124028 + 0.131462i 0.0158802 + 0.0168320i 0.735265 0.677780i \(-0.237058\pi\)
−0.719385 + 0.694612i \(0.755576\pi\)
\(62\) 5.53710 4.64618i 0.703212 0.590065i
\(63\) 0 0
\(64\) 5.37384 + 4.50919i 0.671730 + 0.563648i
\(65\) 0.157509 + 2.70433i 0.0195366 + 0.335431i
\(66\) 0 0
\(67\) −7.95826 10.6898i −0.972256 1.30597i −0.951976 0.306172i \(-0.900952\pi\)
−0.0202796 0.999794i \(-0.506456\pi\)
\(68\) −1.10767 + 0.129468i −0.134324 + 0.0157003i
\(69\) 0 0
\(70\) −3.78311 + 2.48819i −0.452168 + 0.297396i
\(71\) 9.41216 3.42575i 1.11702 0.406561i 0.283455 0.958985i \(-0.408519\pi\)
0.833563 + 0.552424i \(0.186297\pi\)
\(72\) 0 0
\(73\) −10.9327 3.97917i −1.27957 0.465726i −0.389282 0.921119i \(-0.627277\pi\)
−0.890291 + 0.455392i \(0.849499\pi\)
\(74\) 17.3051 4.10138i 2.01168 0.476776i
\(75\) 0 0
\(76\) −0.0578765 + 0.993701i −0.00663889 + 0.113985i
\(77\) 5.29176 5.60894i 0.603052 0.639198i
\(78\) 0 0
\(79\) −1.45390 3.37053i −0.163577 0.379214i 0.816638 0.577150i \(-0.195835\pi\)
−0.980215 + 0.197936i \(0.936576\pi\)
\(80\) −7.00426 −0.783100
\(81\) 0 0
\(82\) 15.0229 1.65900
\(83\) −2.17367 5.03914i −0.238592 0.553117i 0.756282 0.654246i \(-0.227014\pi\)
−0.994873 + 0.101129i \(0.967755\pi\)
\(84\) 0 0
\(85\) −5.95539 + 6.31235i −0.645953 + 0.684670i
\(86\) 0.738510 12.6797i 0.0796356 1.36729i
\(87\) 0 0
\(88\) 10.5124 2.49148i 1.12062 0.265592i
\(89\) −6.65218 2.42120i −0.705130 0.256646i −0.0355305 0.999369i \(-0.511312\pi\)
−0.669600 + 0.742722i \(0.733534\pi\)
\(90\) 0 0
\(91\) −3.02021 + 1.09927i −0.316604 + 0.115234i
\(92\) −0.115251 + 0.0758017i −0.0120157 + 0.00790287i
\(93\) 0 0
\(94\) −0.297508 + 0.0347738i −0.0306857 + 0.00358664i
\(95\) 4.62550 + 6.21312i 0.474566 + 0.637453i
\(96\) 0 0
\(97\) 0.0778051 + 1.33586i 0.00789992 + 0.135636i 0.999952 + 0.00980765i \(0.00312192\pi\)
−0.992052 + 0.125829i \(0.959841\pi\)
\(98\) 3.84894 + 3.22965i 0.388802 + 0.326244i
\(99\) 0 0
\(100\) −0.383526 + 0.321817i −0.0383526 + 0.0321817i
\(101\) −3.40131 3.60518i −0.338443 0.358729i 0.535690 0.844415i \(-0.320051\pi\)
−0.874134 + 0.485686i \(0.838570\pi\)
\(102\) 0 0
\(103\) 1.90445 + 1.25258i 0.187652 + 0.123420i 0.639859 0.768493i \(-0.278993\pi\)
−0.452207 + 0.891913i \(0.649363\pi\)
\(104\) −4.38156 1.03845i −0.429648 0.101828i
\(105\) 0 0
\(106\) −7.32115 0.855719i −0.711092 0.0831148i
\(107\) 2.21467 + 3.83593i 0.214101 + 0.370833i 0.952994 0.302989i \(-0.0979846\pi\)
−0.738893 + 0.673822i \(0.764651\pi\)
\(108\) 0 0
\(109\) −9.21824 + 15.9665i −0.882947 + 1.52931i −0.0348978 + 0.999391i \(0.511111\pi\)
−0.848049 + 0.529918i \(0.822223\pi\)
\(110\) −5.76445 + 7.74301i −0.549619 + 0.738267i
\(111\) 0 0
\(112\) −2.38343 7.96121i −0.225213 0.752264i
\(113\) 8.05934 4.04755i 0.758159 0.380762i −0.0273390 0.999626i \(-0.508703\pi\)
0.785498 + 0.618865i \(0.212407\pi\)
\(114\) 0 0
\(115\) −0.307869 + 1.02835i −0.0287089 + 0.0958944i
\(116\) −0.171216 0.971014i −0.0158970 0.0901563i
\(117\) 0 0
\(118\) 0.489346 2.77522i 0.0450479 0.255479i
\(119\) −9.20129 4.62106i −0.843481 0.423612i
\(120\) 0 0
\(121\) 2.15438 4.99442i 0.195853 0.454038i
\(122\) 0.106323 0.246485i 0.00962604 0.0223157i
\(123\) 0 0
\(124\) −0.895846 0.449911i −0.0804493 0.0404032i
\(125\) −2.06830 + 11.7299i −0.184994 + 1.04915i
\(126\) 0 0
\(127\) −0.304561 1.72725i −0.0270254 0.153269i 0.968309 0.249756i \(-0.0803504\pi\)
−0.995334 + 0.0964872i \(0.969239\pi\)
\(128\) 3.65408 12.2055i 0.322978 1.07882i
\(129\) 0 0
\(130\) 3.59547 1.80571i 0.315344 0.158372i
\(131\) −2.05452 6.86256i −0.179504 0.599585i −0.999625 0.0273945i \(-0.991279\pi\)
0.820121 0.572191i \(-0.193906\pi\)
\(132\) 0 0
\(133\) −5.48801 + 7.37168i −0.475871 + 0.639205i
\(134\) −9.89692 + 17.1420i −0.854964 + 1.48084i
\(135\) 0 0
\(136\) −7.21281 12.4930i −0.618493 1.07126i
\(137\) 17.3549 + 2.02850i 1.48273 + 0.173307i 0.818624 0.574329i \(-0.194737\pi\)
0.664109 + 0.747636i \(0.268811\pi\)
\(138\) 0 0
\(139\) −18.4877 4.38167i −1.56811 0.371649i −0.647478 0.762084i \(-0.724176\pi\)
−0.920630 + 0.390435i \(0.872325\pi\)
\(140\) 0.524681 + 0.345088i 0.0443436 + 0.0291653i
\(141\) 0 0
\(142\) −10.2090 10.8209i −0.856719 0.908069i
\(143\) −5.24886 + 4.40431i −0.438931 + 0.368307i
\(144\) 0 0
\(145\) −5.87767 4.93195i −0.488114 0.409576i
\(146\) 1.00474 + 17.2507i 0.0831528 + 1.42768i
\(147\) 0 0
\(148\) −1.47291 1.97847i −0.121073 0.162629i
\(149\) −7.32320 + 0.855959i −0.599940 + 0.0701229i −0.410642 0.911797i \(-0.634695\pi\)
−0.189298 + 0.981920i \(0.560621\pi\)
\(150\) 0 0
\(151\) 2.23139 1.46761i 0.181588 0.119432i −0.455461 0.890256i \(-0.650525\pi\)
0.637048 + 0.770824i \(0.280155\pi\)
\(152\) −12.0992 + 4.40374i −0.981372 + 0.357190i
\(153\) 0 0
\(154\) −10.7624 3.91721i −0.867262 0.315658i
\(155\) −7.59075 + 1.79904i −0.609704 + 0.144502i
\(156\) 0 0
\(157\) 0.332250 5.70452i 0.0265165 0.455270i −0.958751 0.284248i \(-0.908256\pi\)
0.985267 0.171022i \(-0.0547069\pi\)
\(158\) −3.74138 + 3.96563i −0.297648 + 0.315489i
\(159\) 0 0
\(160\) 0.736981 + 1.70851i 0.0582635 + 0.135070i
\(161\) −1.27361 −0.100375
\(162\) 0 0
\(163\) 16.0381 1.25620 0.628100 0.778132i \(-0.283833\pi\)
0.628100 + 0.778132i \(0.283833\pi\)
\(164\) −0.825242 1.91313i −0.0644406 0.149390i
\(165\) 0 0
\(166\) −5.59359 + 5.92886i −0.434147 + 0.460168i
\(167\) −1.11336 + 19.1157i −0.0861545 + 1.47922i 0.627445 + 0.778661i \(0.284101\pi\)
−0.713599 + 0.700554i \(0.752936\pi\)
\(168\) 0 0
\(169\) −9.87069 + 2.33940i −0.759284 + 0.179954i
\(170\) 12.1121 + 4.40846i 0.928959 + 0.338113i
\(171\) 0 0
\(172\) −1.65530 + 0.602480i −0.126216 + 0.0459387i
\(173\) 19.7483 12.9886i 1.50143 0.987509i 0.509539 0.860448i \(-0.329816\pi\)
0.991895 0.127061i \(-0.0405544\pi\)
\(174\) 0 0
\(175\) −4.59123 + 0.536637i −0.347064 + 0.0405660i
\(176\) −10.5796 14.2108i −0.797464 1.07118i
\(177\) 0 0
\(178\) 0.611352 + 10.4965i 0.0458228 + 0.786747i
\(179\) −3.43489 2.88222i −0.256736 0.215427i 0.505331 0.862926i \(-0.331371\pi\)
−0.762066 + 0.647499i \(0.775815\pi\)
\(180\) 0 0
\(181\) 2.92076 2.45081i 0.217098 0.182167i −0.527752 0.849398i \(-0.676965\pi\)
0.744851 + 0.667231i \(0.232521\pi\)
\(182\) 3.27590 + 3.47225i 0.242826 + 0.257380i
\(183\) 0 0
\(184\) −1.49081 0.980522i −0.109904 0.0722850i
\(185\) −18.6766 4.42643i −1.37313 0.325438i
\(186\) 0 0
\(187\) −21.8023 2.54833i −1.59434 0.186352i
\(188\) 0.0207712 + 0.0359768i 0.00151490 + 0.00262388i
\(189\) 0 0
\(190\) 5.75229 9.96325i 0.417315 0.722810i
\(191\) −10.9862 + 14.7571i −0.794936 + 1.06778i 0.201165 + 0.979557i \(0.435527\pi\)
−0.996100 + 0.0882265i \(0.971880\pi\)
\(192\) 0 0
\(193\) 4.71004 + 15.7326i 0.339036 + 1.13246i 0.942259 + 0.334886i \(0.108698\pi\)
−0.603223 + 0.797573i \(0.706117\pi\)
\(194\) 1.77606 0.891972i 0.127514 0.0640398i
\(195\) 0 0
\(196\) 0.199856 0.667566i 0.0142754 0.0476833i
\(197\) −3.25113 18.4381i −0.231633 1.31366i −0.849589 0.527445i \(-0.823150\pi\)
0.617956 0.786213i \(-0.287961\pi\)
\(198\) 0 0
\(199\) 0.155470 0.881713i 0.0110210 0.0625029i −0.978801 0.204812i \(-0.934342\pi\)
0.989822 + 0.142309i \(0.0454527\pi\)
\(200\) −5.78734 2.90651i −0.409227 0.205521i
\(201\) 0 0
\(202\) −2.91577 + 6.75953i −0.205153 + 0.475599i
\(203\) 3.60571 8.35897i 0.253071 0.586685i
\(204\) 0 0
\(205\) −14.4889 7.27659i −1.01195 0.508219i
\(206\) 0.587899 3.33414i 0.0409609 0.232301i
\(207\) 0 0
\(208\) 1.28226 + 7.27206i 0.0889088 + 0.504227i
\(209\) −5.61912 + 18.7692i −0.388683 + 1.29829i
\(210\) 0 0
\(211\) 13.3695 6.71439i 0.920391 0.462238i 0.0754817 0.997147i \(-0.475951\pi\)
0.844909 + 0.534909i \(0.179654\pi\)
\(212\) 0.293194 + 0.979338i 0.0201367 + 0.0672612i
\(213\) 0 0
\(214\) 3.92854 5.27695i 0.268550 0.360725i
\(215\) −6.85392 + 11.8713i −0.467433 + 0.809618i
\(216\) 0 0
\(217\) −4.62784 8.01565i −0.314158 0.544138i
\(218\) 27.1978 + 3.17896i 1.84206 + 0.215306i
\(219\) 0 0
\(220\) 1.30271 + 0.308748i 0.0878286 + 0.0208158i
\(221\) 7.64395 + 5.02750i 0.514188 + 0.338186i
\(222\) 0 0
\(223\) 4.25530 + 4.51035i 0.284956 + 0.302036i 0.854002 0.520270i \(-0.174169\pi\)
−0.569046 + 0.822306i \(0.692687\pi\)
\(224\) −1.69116 + 1.41905i −0.112995 + 0.0948142i
\(225\) 0 0
\(226\) −10.2612 8.61013i −0.682562 0.572737i
\(227\) −0.830506 14.2592i −0.0551226 0.946419i −0.906590 0.422012i \(-0.861324\pi\)
0.851468 0.524407i \(-0.175713\pi\)
\(228\) 0 0
\(229\) 11.6644 + 15.6680i 0.770804 + 1.03537i 0.998104 + 0.0615447i \(0.0196027\pi\)
−0.227300 + 0.973825i \(0.572990\pi\)
\(230\) 1.58357 0.185093i 0.104417 0.0122046i
\(231\) 0 0
\(232\) 10.6560 7.00853i 0.699598 0.460133i
\(233\) 8.91628 3.24526i 0.584125 0.212604i −0.0330187 0.999455i \(-0.510512\pi\)
0.617143 + 0.786851i \(0.288290\pi\)
\(234\) 0 0
\(235\) 0.303777 + 0.110566i 0.0198162 + 0.00721252i
\(236\) −0.380298 + 0.0901324i −0.0247553 + 0.00586712i
\(237\) 0 0
\(238\) −0.889207 + 15.2671i −0.0576387 + 0.989619i
\(239\) −7.55122 + 8.00383i −0.488448 + 0.517725i −0.923976 0.382451i \(-0.875080\pi\)
0.435528 + 0.900175i \(0.356562\pi\)
\(240\) 0 0
\(241\) −0.867612 2.01135i −0.0558878 0.129562i 0.887984 0.459874i \(-0.152105\pi\)
−0.943872 + 0.330312i \(0.892846\pi\)
\(242\) −8.07871 −0.519319
\(243\) 0 0
\(244\) −0.0372298 −0.00238340
\(245\) −2.14780 4.97916i −0.137218 0.318107i
\(246\) 0 0
\(247\) 5.60389 5.93978i 0.356567 0.377939i
\(248\) 0.753987 12.9455i 0.0478782 0.822038i
\(249\) 0 0
\(250\) 17.2138 4.07975i 1.08870 0.258026i
\(251\) 6.59388 + 2.39998i 0.416202 + 0.151485i 0.541629 0.840618i \(-0.317808\pi\)
−0.125427 + 0.992103i \(0.540030\pi\)
\(252\) 0 0
\(253\) −2.55143 + 0.928643i −0.160407 + 0.0583833i
\(254\) −2.17644 + 1.43147i −0.136562 + 0.0898181i
\(255\) 0 0
\(256\) −4.86005 + 0.568059i −0.303753 + 0.0355037i
\(257\) −0.279271 0.375126i −0.0174205 0.0233997i 0.793328 0.608795i \(-0.208347\pi\)
−0.810748 + 0.585395i \(0.800939\pi\)
\(258\) 0 0
\(259\) −1.32414 22.7345i −0.0822778 1.41265i
\(260\) −0.427461 0.358683i −0.0265100 0.0222446i
\(261\) 0 0
\(262\) −8.15045 + 6.83904i −0.503536 + 0.422517i
\(263\) −13.0974 13.8824i −0.807621 0.856028i 0.184302 0.982870i \(-0.440997\pi\)
−0.991923 + 0.126842i \(0.959516\pi\)
\(264\) 0 0
\(265\) 6.64644 + 4.37143i 0.408288 + 0.268535i
\(266\) 13.2819 + 3.14787i 0.814365 + 0.193008i
\(267\) 0 0
\(268\) 2.72665 + 0.318700i 0.166557 + 0.0194677i
\(269\) −2.12061 3.67300i −0.129296 0.223947i 0.794108 0.607776i \(-0.207938\pi\)
−0.923404 + 0.383830i \(0.874605\pi\)
\(270\) 0 0
\(271\) −3.83162 + 6.63656i −0.232754 + 0.403142i −0.958618 0.284697i \(-0.908107\pi\)
0.725863 + 0.687839i \(0.241440\pi\)
\(272\) −14.1265 + 18.9752i −0.856544 + 1.15054i
\(273\) 0 0
\(274\) −7.44313 24.8618i −0.449656 1.50196i
\(275\) −8.80630 + 4.42269i −0.531040 + 0.266698i
\(276\) 0 0
\(277\) −4.25476 + 14.2119i −0.255644 + 0.853909i 0.729764 + 0.683699i \(0.239630\pi\)
−0.985408 + 0.170210i \(0.945555\pi\)
\(278\) 4.90030 + 27.7910i 0.293901 + 1.66679i
\(279\) 0 0
\(280\) −1.41060 + 7.99991i −0.0842995 + 0.478086i
\(281\) 0.994631 + 0.499522i 0.0593347 + 0.0297990i 0.478219 0.878241i \(-0.341282\pi\)
−0.418884 + 0.908040i \(0.637579\pi\)
\(282\) 0 0
\(283\) −2.61783 + 6.06882i −0.155614 + 0.360754i −0.978132 0.207985i \(-0.933309\pi\)
0.822518 + 0.568739i \(0.192569\pi\)
\(284\) −0.817211 + 1.89451i −0.0484926 + 0.112418i
\(285\) 0 0
\(286\) 9.09435 + 4.56735i 0.537760 + 0.270073i
\(287\) 3.34043 18.9445i 0.197179 1.11826i
\(288\) 0 0
\(289\) 2.13761 + 12.1230i 0.125742 + 0.713117i
\(290\) −3.26841 + 10.9173i −0.191928 + 0.641084i
\(291\) 0 0
\(292\) 2.14165 1.07557i 0.125330 0.0629432i
\(293\) −0.892759 2.98202i −0.0521555 0.174212i 0.927943 0.372721i \(-0.121575\pi\)
−0.980099 + 0.198509i \(0.936390\pi\)
\(294\) 0 0
\(295\) −1.81618 + 2.43955i −0.105742 + 0.142036i
\(296\) 15.9528 27.6310i 0.927235 1.60602i
\(297\) 0 0
\(298\) 5.47544 + 9.48374i 0.317184 + 0.549379i
\(299\) 1.12403 + 0.131381i 0.0650045 + 0.00759794i
\(300\) 0 0
\(301\) −15.8255 3.75072i −0.912168 0.216188i
\(302\) −3.31418 2.17977i −0.190710 0.125432i
\(303\) 0 0
\(304\) 14.4896 + 15.3581i 0.831037 + 0.880848i
\(305\) −0.221933 + 0.186224i −0.0127079 + 0.0106632i
\(306\) 0 0
\(307\) −5.76257 4.83537i −0.328887 0.275969i 0.463359 0.886171i \(-0.346644\pi\)
−0.792246 + 0.610202i \(0.791088\pi\)
\(308\) 0.0923596 + 1.58575i 0.00526268 + 0.0903567i
\(309\) 0 0
\(310\) 6.91900 + 9.29383i 0.392973 + 0.527854i
\(311\) 15.2831 1.78634i 0.866628 0.101294i 0.328851 0.944382i \(-0.393338\pi\)
0.537777 + 0.843087i \(0.319264\pi\)
\(312\) 0 0
\(313\) 3.31693 2.18158i 0.187484 0.123310i −0.452297 0.891867i \(-0.649395\pi\)
0.639781 + 0.768557i \(0.279025\pi\)
\(314\) −7.97521 + 2.90274i −0.450067 + 0.163811i
\(315\) 0 0
\(316\) 0.710537 + 0.258614i 0.0399708 + 0.0145482i
\(317\) 8.34397 1.97756i 0.468644 0.111071i 0.0104930 0.999945i \(-0.496660\pi\)
0.458151 + 0.888874i \(0.348512\pi\)
\(318\) 0 0
\(319\) 1.12844 19.3746i 0.0631805 1.08477i
\(320\) −7.71673 + 8.17925i −0.431378 + 0.457234i
\(321\) 0 0
\(322\) 0.749242 + 1.73694i 0.0417536 + 0.0967958i
\(323\) 26.1608 1.45563
\(324\) 0 0
\(325\) 4.10736 0.227835
\(326\) −9.43490 21.8726i −0.522551 1.21141i
\(327\) 0 0
\(328\) 18.4950 19.6035i 1.02121 1.08242i
\(329\) −0.0223016 + 0.382905i −0.00122953 + 0.0211102i
\(330\) 0 0
\(331\) −9.07927 + 2.15183i −0.499042 + 0.118275i −0.472425 0.881371i \(-0.656621\pi\)
−0.0266164 + 0.999646i \(0.508473\pi\)
\(332\) 1.06230 + 0.386644i 0.0583010 + 0.0212198i
\(333\) 0 0
\(334\) 26.7247 9.72699i 1.46231 0.532237i
\(335\) 17.8482 11.7389i 0.975150 0.641366i
\(336\) 0 0
\(337\) −4.37776 + 0.511687i −0.238472 + 0.0278734i −0.234489 0.972119i \(-0.575342\pi\)
−0.00398267 + 0.999992i \(0.501268\pi\)
\(338\) 8.99717 + 12.0853i 0.489382 + 0.657354i
\(339\) 0 0
\(340\) −0.103942 1.78462i −0.00563706 0.0967847i
\(341\) −15.1155 12.6834i −0.818548 0.686844i
\(342\) 0 0
\(343\) 15.1270 12.6931i 0.816782 0.685362i
\(344\) −15.6368 16.5740i −0.843078 0.893610i
\(345\) 0 0
\(346\) −29.3313 19.2915i −1.57686 1.03712i
\(347\) 19.4982 + 4.62117i 1.04672 + 0.248077i 0.717777 0.696273i \(-0.245160\pi\)
0.328943 + 0.944350i \(0.393308\pi\)
\(348\) 0 0
\(349\) 33.4202 + 3.90626i 1.78894 + 0.209097i 0.944939 0.327245i \(-0.106120\pi\)
0.844001 + 0.536342i \(0.180194\pi\)
\(350\) 3.43279 + 5.94576i 0.183490 + 0.317814i
\(351\) 0 0
\(352\) −2.35320 + 4.07587i −0.125426 + 0.217244i
\(353\) 4.81620 6.46927i 0.256340 0.344325i −0.655259 0.755404i \(-0.727441\pi\)
0.911600 + 0.411079i \(0.134848\pi\)
\(354\) 0 0
\(355\) 4.60483 + 15.3812i 0.244399 + 0.816349i
\(356\) 1.30312 0.654453i 0.0690654 0.0346859i
\(357\) 0 0
\(358\) −1.91005 + 6.38002i −0.100949 + 0.337194i
\(359\) −2.83469 16.0764i −0.149609 0.848477i −0.963550 0.267529i \(-0.913793\pi\)
0.813940 0.580948i \(-0.197318\pi\)
\(360\) 0 0
\(361\) 0.755367 4.28390i 0.0397562 0.225468i
\(362\) −5.06061 2.54153i −0.265980 0.133580i
\(363\) 0 0
\(364\) 0.262230 0.607917i 0.0137446 0.0318635i
\(365\) 7.38667 17.1242i 0.386636 0.896323i
\(366\) 0 0
\(367\) 11.7615 + 5.90686i 0.613947 + 0.308336i 0.728462 0.685086i \(-0.240235\pi\)
−0.114516 + 0.993421i \(0.536532\pi\)
\(368\) −0.508116 + 2.88167i −0.0264874 + 0.150217i
\(369\) 0 0
\(370\) 4.95036 + 28.0749i 0.257357 + 1.45954i
\(371\) −2.70701 + 9.04204i −0.140541 + 0.469439i
\(372\) 0 0
\(373\) 0.194504 0.0976835i 0.0100710 0.00505786i −0.443757 0.896147i \(-0.646354\pi\)
0.453828 + 0.891090i \(0.350058\pi\)
\(374\) 9.35050 + 31.2329i 0.483503 + 1.61501i
\(375\) 0 0
\(376\) −0.320893 + 0.431034i −0.0165488 + 0.0222289i
\(377\) −4.04451 + 7.00529i −0.208303 + 0.360791i
\(378\) 0 0
\(379\) 12.0931 + 20.9458i 0.621180 + 1.07592i 0.989266 + 0.146124i \(0.0466797\pi\)
−0.368086 + 0.929792i \(0.619987\pi\)
\(380\) −1.58478 0.185235i −0.0812977 0.00950234i
\(381\) 0 0
\(382\) 26.5885 + 6.30159i 1.36039 + 0.322417i
\(383\) 7.06738 + 4.64829i 0.361126 + 0.237516i 0.717086 0.696985i \(-0.245476\pi\)
−0.355960 + 0.934501i \(0.615846\pi\)
\(384\) 0 0
\(385\) 8.48253 + 8.99096i 0.432310 + 0.458222i
\(386\) 18.6851 15.6787i 0.951048 0.798024i
\(387\) 0 0
\(388\) −0.211154 0.177179i −0.0107197 0.00899491i
\(389\) 1.46030 + 25.0723i 0.0740400 + 1.27122i 0.806839 + 0.590772i \(0.201177\pi\)
−0.732799 + 0.680446i \(0.761786\pi\)
\(390\) 0 0
\(391\) 2.16498 + 2.90807i 0.109488 + 0.147067i
\(392\) 8.95294 1.04645i 0.452192 0.0528536i
\(393\) 0 0
\(394\) −23.2330 + 15.2806i −1.17046 + 0.769826i
\(395\) 5.52922 2.01247i 0.278205 0.101258i
\(396\) 0 0
\(397\) 23.8173 + 8.66880i 1.19536 + 0.435074i 0.861602 0.507585i \(-0.169462\pi\)
0.333756 + 0.942660i \(0.391684\pi\)
\(398\) −1.29393 + 0.306667i −0.0648588 + 0.0153718i
\(399\) 0 0
\(400\) −0.617506 + 10.6022i −0.0308753 + 0.530108i
\(401\) 16.2900 17.2664i 0.813483 0.862242i −0.179097 0.983831i \(-0.557318\pi\)
0.992580 + 0.121589i \(0.0387991\pi\)
\(402\) 0 0
\(403\) 3.25746 + 7.55163i 0.162265 + 0.376174i
\(404\) 1.02098 0.0507957
\(405\) 0 0
\(406\) −13.5210 −0.671037
\(407\) −19.2293 44.5785i −0.953160 2.20967i
\(408\) 0 0
\(409\) −6.44213 + 6.82826i −0.318543 + 0.337636i −0.866783 0.498685i \(-0.833816\pi\)
0.548240 + 0.836321i \(0.315298\pi\)
\(410\) −1.40020 + 24.0404i −0.0691508 + 1.18727i
\(411\) 0 0
\(412\) −0.456890 + 0.108285i −0.0225093 + 0.00533481i
\(413\) −3.39087 1.23418i −0.166854 0.0607298i
\(414\) 0 0
\(415\) 8.26652 3.00877i 0.405787 0.147695i
\(416\) 1.63892 1.07794i 0.0803547 0.0528501i
\(417\) 0 0
\(418\) 28.9028 3.37825i 1.41368 0.165236i
\(419\) −7.01065 9.41694i −0.342493 0.460048i 0.597187 0.802102i \(-0.296285\pi\)
−0.939680 + 0.342054i \(0.888877\pi\)
\(420\) 0 0
\(421\) −0.393410 6.75459i −0.0191736 0.329199i −0.994232 0.107250i \(-0.965795\pi\)
0.975058 0.221948i \(-0.0712416\pi\)
\(422\) −17.0220 14.2831i −0.828618 0.695293i
\(423\) 0 0
\(424\) −10.1299 + 8.49998i −0.491950 + 0.412795i
\(425\) 9.02980 + 9.57103i 0.438010 + 0.464263i
\(426\) 0 0
\(427\) −0.287187 0.188886i −0.0138980 0.00914083i
\(428\) −0.887812 0.210415i −0.0429140 0.0101708i
\(429\) 0 0
\(430\) 20.2220 + 2.36361i 0.975191 + 0.113984i
\(431\) 3.90563 + 6.76475i 0.188128 + 0.325846i 0.944626 0.328149i \(-0.106425\pi\)
−0.756498 + 0.653996i \(0.773092\pi\)
\(432\) 0 0
\(433\) −2.20878 + 3.82573i −0.106147 + 0.183853i −0.914206 0.405249i \(-0.867185\pi\)
0.808059 + 0.589102i \(0.200518\pi\)
\(434\) −8.20918 + 11.0268i −0.394053 + 0.529305i
\(435\) 0 0
\(436\) −1.08921 3.63820i −0.0521635 0.174238i
\(437\) 2.89173 1.45228i 0.138330 0.0694721i
\(438\) 0 0
\(439\) 4.31161 14.4018i 0.205782 0.687360i −0.791328 0.611392i \(-0.790610\pi\)
0.997110 0.0759684i \(-0.0242048\pi\)
\(440\) 3.00721 + 17.0547i 0.143363 + 0.813052i
\(441\) 0 0
\(442\) 2.35966 13.3823i 0.112238 0.636531i
\(443\) 10.1485 + 5.09675i 0.482168 + 0.242154i 0.673243 0.739422i \(-0.264901\pi\)
−0.191075 + 0.981576i \(0.561197\pi\)
\(444\) 0 0
\(445\) 4.49455 10.4195i 0.213062 0.493934i
\(446\) 3.64786 8.45668i 0.172731 0.400435i
\(447\) 0 0
\(448\) −11.9226 5.98776i −0.563291 0.282895i
\(449\) −1.16004 + 6.57891i −0.0547457 + 0.310478i −0.999868 0.0162381i \(-0.994831\pi\)
0.945122 + 0.326716i \(0.105942\pi\)
\(450\) 0 0
\(451\) −7.12134 40.3871i −0.335331 1.90176i
\(452\) −0.532810 + 1.77971i −0.0250613 + 0.0837105i
\(453\) 0 0
\(454\) −18.9580 + 9.52106i −0.889743 + 0.446846i
\(455\) −1.47761 4.93557i −0.0692716 0.231383i
\(456\) 0 0
\(457\) 7.17351 9.63570i 0.335563 0.450739i −0.602030 0.798473i \(-0.705641\pi\)
0.937593 + 0.347734i \(0.113049\pi\)
\(458\) 14.5059 25.1249i 0.677815 1.17401i
\(459\) 0 0
\(460\) −0.110560 0.191496i −0.00515490 0.00892855i
\(461\) −6.95142 0.812504i −0.323760 0.0378421i −0.0473393 0.998879i \(-0.515074\pi\)
−0.276421 + 0.961037i \(0.589148\pi\)
\(462\) 0 0
\(463\) 27.2778 + 6.46495i 1.26771 + 0.300452i 0.808827 0.588047i \(-0.200103\pi\)
0.458879 + 0.888499i \(0.348251\pi\)
\(464\) −17.4744 11.4931i −0.811229 0.533554i
\(465\) 0 0
\(466\) −9.67112 10.2508i −0.448006 0.474858i
\(467\) −10.9662 + 9.20178i −0.507458 + 0.425807i −0.860233 0.509900i \(-0.829682\pi\)
0.352776 + 0.935708i \(0.385238\pi\)
\(468\) 0 0
\(469\) 19.4162 + 16.2921i 0.896557 + 0.752300i
\(470\) −0.0279179 0.479331i −0.00128776 0.0221099i
\(471\) 0 0
\(472\) −3.01898 4.05519i −0.138960 0.186655i
\(473\) −34.4380 + 4.02523i −1.58346 + 0.185080i
\(474\) 0 0
\(475\) 9.81243 6.45374i 0.450225 0.296118i
\(476\) 1.99307 0.725420i 0.0913524 0.0332496i
\(477\) 0 0
\(478\) 15.3578 + 5.58977i 0.702448 + 0.255670i
\(479\) −21.8904 + 5.18813i −1.00020 + 0.237052i −0.697926 0.716170i \(-0.745894\pi\)
−0.302273 + 0.953221i \(0.597745\pi\)
\(480\) 0 0
\(481\) −1.17658 + 20.2010i −0.0536473 + 0.921088i
\(482\) −2.23266 + 2.36648i −0.101695 + 0.107790i
\(483\) 0 0
\(484\) 0.443783 + 1.02881i 0.0201720 + 0.0467639i
\(485\) −2.14498 −0.0973984
\(486\) 0 0
\(487\) −41.7203 −1.89053 −0.945264 0.326307i \(-0.894196\pi\)
−0.945264 + 0.326307i \(0.894196\pi\)
\(488\) −0.190745 0.442196i −0.00863460 0.0200173i
\(489\) 0 0
\(490\) −5.52701 + 5.85829i −0.249685 + 0.264650i
\(491\) 0.643607 11.0503i 0.0290456 0.498694i −0.952144 0.305649i \(-0.901127\pi\)
0.981190 0.193045i \(-0.0618363\pi\)
\(492\) 0 0
\(493\) −25.2154 + 5.97617i −1.13565 + 0.269153i
\(494\) −11.3973 4.14826i −0.512787 0.186639i
\(495\) 0 0
\(496\) −19.9825 + 7.27302i −0.897239 + 0.326568i
\(497\) −15.9157 + 10.4679i −0.713917 + 0.469550i
\(498\) 0 0
\(499\) −7.76171 + 0.907214i −0.347462 + 0.0406125i −0.288034 0.957620i \(-0.593002\pi\)
−0.0594278 + 0.998233i \(0.518928\pi\)
\(500\) −1.46514 1.96803i −0.0655232 0.0880130i
\(501\) 0 0
\(502\) −0.605994 10.4045i −0.0270468 0.464376i
\(503\) 18.1547 + 15.2336i 0.809478 + 0.679233i 0.950483 0.310776i \(-0.100589\pi\)
−0.141005 + 0.990009i \(0.545033\pi\)
\(504\) 0 0
\(505\) 6.08624 5.10696i 0.270834 0.227257i
\(506\) 2.76743 + 2.93330i 0.123027 + 0.130401i
\(507\) 0 0
\(508\) 0.301851 + 0.198530i 0.0133925 + 0.00880836i
\(509\) 12.1281 + 2.87442i 0.537570 + 0.127406i 0.490428 0.871482i \(-0.336841\pi\)
0.0471419 + 0.998888i \(0.484989\pi\)
\(510\) 0 0
\(511\) 21.9774 + 2.56879i 0.972222 + 0.113636i
\(512\) −9.10692 15.7736i −0.402473 0.697103i
\(513\) 0 0
\(514\) −0.347303 + 0.601546i −0.0153189 + 0.0265331i
\(515\) −2.18195 + 2.93087i −0.0961484 + 0.129150i
\(516\) 0 0
\(517\) 0.234514 + 0.783332i 0.0103139 + 0.0344509i
\(518\) −30.2261 + 15.1801i −1.32806 + 0.666976i
\(519\) 0 0
\(520\) 2.07017 6.91484i 0.0907829 0.303236i
\(521\) 3.66734 + 20.7985i 0.160669 + 0.911200i 0.953418 + 0.301652i \(0.0975380\pi\)
−0.792749 + 0.609548i \(0.791351\pi\)
\(522\) 0 0
\(523\) 7.23247 41.0174i 0.316254 1.79356i −0.248848 0.968543i \(-0.580052\pi\)
0.565102 0.825021i \(-0.308837\pi\)
\(524\) 1.31866 + 0.662256i 0.0576059 + 0.0289308i
\(525\) 0 0
\(526\) −11.2277 + 26.0288i −0.489553 + 1.13491i
\(527\) −10.4356 + 24.1924i −0.454581 + 1.05384i
\(528\) 0 0
\(529\) −20.1528 10.1211i −0.876209 0.440049i
\(530\) 2.05173 11.6360i 0.0891217 0.505434i
\(531\) 0 0
\(532\) −0.328733 1.86434i −0.0142524 0.0808293i
\(533\) −4.90235 + 16.3750i −0.212344 + 0.709279i
\(534\) 0 0
\(535\) −6.34489 + 3.18653i −0.274314 + 0.137766i
\(536\) 10.1845 + 34.0185i 0.439902 + 1.46938i
\(537\) 0 0
\(538\) −3.76168 + 5.05281i −0.162177 + 0.217842i
\(539\) 6.85799 11.8784i 0.295395 0.511638i
\(540\) 0 0
\(541\) −4.87647 8.44629i −0.209656 0.363134i 0.741950 0.670455i \(-0.233901\pi\)
−0.951606 + 0.307320i \(0.900568\pi\)
\(542\) 11.3049 + 1.32136i 0.485588 + 0.0567571i
\(543\) 0 0
\(544\) 6.11490 + 1.44926i 0.262174 + 0.0621364i
\(545\) −24.6913 16.2397i −1.05766 0.695632i
\(546\) 0 0
\(547\) −0.475687 0.504198i −0.0203389 0.0215580i 0.717124 0.696945i \(-0.245458\pi\)
−0.737463 + 0.675387i \(0.763976\pi\)
\(548\) −2.75722 + 2.31358i −0.117783 + 0.0988314i
\(549\) 0 0
\(550\) 11.2122 + 9.40814i 0.478089 + 0.401164i
\(551\) 1.34487 + 23.0905i 0.0572934 + 0.983689i
\(552\) 0 0
\(553\) 4.16893 + 5.59984i 0.177281 + 0.238130i
\(554\) 21.8850 2.55799i 0.929804 0.108678i
\(555\) 0 0
\(556\) 3.26993 2.15067i 0.138676 0.0912087i
\(557\) −28.7125 + 10.4505i −1.21659 + 0.442801i −0.868984 0.494841i \(-0.835226\pi\)
−0.347602 + 0.937642i \(0.613004\pi\)
\(558\) 0 0
\(559\) 13.5800 + 4.94270i 0.574371 + 0.209054i
\(560\) 12.9621 3.07208i 0.547751 0.129819i
\(561\) 0 0
\(562\) 0.0961204 1.65032i 0.00405460 0.0696147i
\(563\) 6.68923 7.09017i 0.281918 0.298815i −0.570905 0.821016i \(-0.693407\pi\)
0.852822 + 0.522201i \(0.174889\pi\)
\(564\) 0 0
\(565\) 5.72596 + 13.2743i 0.240893 + 0.558453i
\(566\) 9.81660 0.412622
\(567\) 0 0
\(568\) −26.6889 −1.11984
\(569\) −7.79560 18.0722i −0.326808 0.757627i −0.999838 0.0180113i \(-0.994267\pi\)
0.673029 0.739616i \(-0.264993\pi\)
\(570\) 0 0
\(571\) 22.6458 24.0031i 0.947697 1.00450i −0.0522860 0.998632i \(-0.516651\pi\)
0.999983 0.00586776i \(-0.00186778\pi\)
\(572\) 0.0820673 1.40904i 0.00343140 0.0589149i
\(573\) 0 0
\(574\) −27.8014 + 6.58906i −1.16041 + 0.275022i
\(575\) 1.52945 + 0.556674i 0.0637824 + 0.0232149i
\(576\) 0 0
\(577\) −19.1279 + 6.96197i −0.796303 + 0.289831i −0.707954 0.706259i \(-0.750381\pi\)
−0.0883494 + 0.996090i \(0.528159\pi\)
\(578\) 15.2757 10.0470i 0.635384 0.417899i
\(579\) 0 0
\(580\) 1.56983 0.183487i 0.0651837 0.00761888i
\(581\) 6.23280 + 8.37210i 0.258580 + 0.347333i
\(582\) 0 0
\(583\) 1.16997 + 20.0877i 0.0484553 + 0.831946i
\(584\) 23.7477 + 19.9267i 0.982686 + 0.824571i
\(585\) 0 0
\(586\) −3.54165 + 2.97180i −0.146304 + 0.122764i
\(587\) 24.1185 + 25.5641i 0.995477 + 1.05514i 0.998478 + 0.0551480i \(0.0175631\pi\)
−0.00300161 + 0.999995i \(0.500955\pi\)
\(588\) 0 0
\(589\) 19.6476 + 12.9224i 0.809566 + 0.532460i
\(590\) 4.39545 + 1.04174i 0.180958 + 0.0428878i
\(591\) 0 0
\(592\) −51.9672 6.07410i −2.13584 0.249644i
\(593\) −4.46816 7.73909i −0.183485 0.317806i 0.759580 0.650414i \(-0.225405\pi\)
−0.943065 + 0.332608i \(0.892071\pi\)
\(594\) 0 0
\(595\) 8.25249 14.2937i 0.338319 0.585986i
\(596\) 0.906953 1.21825i 0.0371503 0.0499015i
\(597\) 0 0
\(598\) −0.482071 1.61023i −0.0197134 0.0658472i
\(599\) −35.4506 + 17.8040i −1.44847 + 0.727451i −0.987152 0.159782i \(-0.948921\pi\)
−0.461322 + 0.887233i \(0.652625\pi\)
\(600\) 0 0
\(601\) −6.78673 + 22.6693i −0.276837 + 0.924699i 0.700615 + 0.713539i \(0.252909\pi\)
−0.977452 + 0.211159i \(0.932276\pi\)
\(602\) 4.19466 + 23.7891i 0.170962 + 0.969572i
\(603\) 0 0
\(604\) −0.0955328 + 0.541794i −0.00388718 + 0.0220453i
\(605\) 7.79156 + 3.91307i 0.316772 + 0.159089i
\(606\) 0 0
\(607\) 7.03429 16.3073i 0.285513 0.661893i −0.713745 0.700405i \(-0.753003\pi\)
0.999258 + 0.0385121i \(0.0122618\pi\)
\(608\) 2.22164 5.15035i 0.0900995 0.208874i
\(609\) 0 0
\(610\) 0.384529 + 0.193118i 0.0155691 + 0.00781911i
\(611\) 0.0591812 0.335633i 0.00239422 0.0135783i
\(612\) 0 0
\(613\) −0.410662 2.32898i −0.0165865 0.0940666i 0.975391 0.220483i \(-0.0707635\pi\)
−0.991977 + 0.126417i \(0.959652\pi\)
\(614\) −3.20441 + 10.7035i −0.129319 + 0.431957i
\(615\) 0 0
\(616\) −18.3615 + 9.22150i −0.739807 + 0.371545i
\(617\) −9.69418 32.3808i −0.390273 1.30360i −0.897204 0.441616i \(-0.854405\pi\)
0.506931 0.861986i \(-0.330780\pi\)
\(618\) 0 0
\(619\) 28.3599 38.0940i 1.13988 1.53113i 0.330537 0.943793i \(-0.392770\pi\)
0.809345 0.587334i \(-0.199823\pi\)
\(620\) 0.803470 1.39165i 0.0322681 0.0558901i
\(621\) 0 0
\(622\) −11.4270 19.7921i −0.458180 0.793591i
\(623\) 13.3725 + 1.56303i 0.535759 + 0.0626213i
\(624\) 0 0
\(625\) −6.75322 1.60054i −0.270129 0.0640217i
\(626\) −4.92649 3.24021i −0.196902 0.129505i
\(627\) 0 0
\(628\) 0.807755 + 0.856170i 0.0322329 + 0.0341649i
\(629\) −49.6594 + 41.6692i −1.98005 + 1.66146i
\(630\) 0 0
\(631\) −14.6874 12.3242i −0.584695 0.490617i 0.301790 0.953374i \(-0.402416\pi\)
−0.886485 + 0.462757i \(0.846860\pi\)
\(632\) 0.568709 + 9.76436i 0.0226220 + 0.388406i
\(633\) 0 0
\(634\) −7.60557 10.2161i −0.302056 0.405731i
\(635\) 2.79244 0.326389i 0.110814 0.0129523i
\(636\) 0 0
\(637\) −4.77634 + 3.14145i −0.189246 + 0.124469i
\(638\) −27.0866 + 9.85872i −1.07237 + 0.390311i
\(639\) 0 0
\(640\) 19.1913 + 6.98507i 0.758603 + 0.276109i
\(641\) 2.04822 0.485436i 0.0808997 0.0191736i −0.189967 0.981791i \(-0.560838\pi\)
0.270866 + 0.962617i \(0.412690\pi\)
\(642\) 0 0
\(643\) 2.54772 43.7427i 0.100472 1.72504i −0.452433 0.891798i \(-0.649444\pi\)
0.552905 0.833244i \(-0.313519\pi\)
\(644\) 0.180037 0.190829i 0.00709447 0.00751970i
\(645\) 0 0
\(646\) −15.3899 35.6778i −0.605507 1.40372i
\(647\) 2.17952 0.0856859 0.0428430 0.999082i \(-0.486358\pi\)
0.0428430 + 0.999082i \(0.486358\pi\)
\(648\) 0 0
\(649\) −7.69281 −0.301969
\(650\) −2.41628 5.60157i −0.0947743 0.219712i
\(651\) 0 0
\(652\) −2.26714 + 2.40303i −0.0887880 + 0.0941098i
\(653\) 1.08815 18.6828i 0.0425826 0.731115i −0.907680 0.419664i \(-0.862148\pi\)
0.950262 0.311451i \(-0.100815\pi\)
\(654\) 0 0
\(655\) 11.1734 2.64814i 0.436579 0.103471i
\(656\) −41.5311 15.1161i −1.62152 0.590183i
\(657\) 0 0
\(658\) 0.535320 0.194841i 0.0208689 0.00759568i
\(659\) 11.9512 7.86043i 0.465553 0.306199i −0.294974 0.955505i \(-0.595311\pi\)
0.760527 + 0.649306i \(0.224941\pi\)
\(660\) 0 0
\(661\) −24.8243 + 2.90155i −0.965555 + 0.112857i −0.584234 0.811586i \(-0.698605\pi\)
−0.381321 + 0.924443i \(0.624531\pi\)
\(662\) 8.27579 + 11.1163i 0.321648 + 0.432048i
\(663\) 0 0
\(664\) 0.850255 + 14.5983i 0.0329963 + 0.566524i
\(665\) −11.2851 9.46931i −0.437617 0.367204i
\(666\) 0 0
\(667\) −2.45548 + 2.06039i −0.0950764 + 0.0797786i
\(668\) −2.70676 2.86900i −0.104728 0.111005i
\(669\) 0 0
\(670\) −26.5091 17.4353i −1.02414 0.673586i
\(671\) −0.713045 0.168995i −0.0275268 0.00652397i
\(672\) 0 0
\(673\) 29.4895 + 3.44683i 1.13674 + 0.132866i 0.663576 0.748109i \(-0.269038\pi\)
0.473163 + 0.880975i \(0.343112\pi\)
\(674\) 3.27319 + 5.66933i 0.126078 + 0.218374i
\(675\) 0 0
\(676\) 1.04480 1.80964i 0.0401846 0.0696017i
\(677\) 23.1605 31.1099i 0.890129 1.19565i −0.0897310 0.995966i \(-0.528601\pi\)
0.979860 0.199685i \(-0.0639919\pi\)
\(678\) 0 0
\(679\) −0.729900 2.43803i −0.0280110 0.0935632i
\(680\) 20.6642 10.3780i 0.792436 0.397977i
\(681\) 0 0
\(682\) −8.40530 + 28.0757i −0.321856 + 1.07507i
\(683\) −2.81006 15.9367i −0.107524 0.609799i −0.990182 0.139784i \(-0.955359\pi\)
0.882658 0.470016i \(-0.155752\pi\)
\(684\) 0 0
\(685\) −4.86369 + 27.5833i −0.185832 + 1.05391i
\(686\) −26.2096 13.1630i −1.00069 0.502564i
\(687\) 0 0
\(688\) −14.8000 + 34.3103i −0.564246 + 1.30807i
\(689\) 3.32182 7.70084i 0.126551 0.293379i
\(690\) 0 0
\(691\) −15.7344 7.90210i −0.598564 0.300610i 0.123600 0.992332i \(-0.460556\pi\)
−0.722164 + 0.691722i \(0.756852\pi\)
\(692\) −0.845488 + 4.79500i −0.0321406 + 0.182279i
\(693\) 0 0
\(694\) −5.16814 29.3100i −0.196180 1.11259i
\(695\) 8.73495 29.1768i 0.331335 1.10674i
\(696\) 0 0
\(697\) −48.9348 + 24.5760i −1.85354 + 0.930881i
\(698\) −14.3331 47.8760i −0.542517 1.81213i
\(699\) 0 0
\(700\) 0.568608 0.763773i 0.0214914 0.0288679i
\(701\) −9.33660 + 16.1715i −0.352639 + 0.610788i −0.986711 0.162486i \(-0.948049\pi\)
0.634072 + 0.773274i \(0.281382\pi\)
\(702\) 0 0
\(703\) 28.9303 + 50.1087i 1.09113 + 1.88989i
\(704\) −28.2504 3.30200i −1.06473 0.124449i
\(705\) 0 0
\(706\) −11.6560 2.76252i −0.438679 0.103969i
\(707\) 7.87574 + 5.17996i 0.296198 + 0.194812i
\(708\) 0 0
\(709\) −22.6076 23.9627i −0.849047 0.899938i 0.146966 0.989142i \(-0.453049\pi\)
−0.996013 + 0.0892040i \(0.971568\pi\)
\(710\) 18.2677 15.3285i 0.685576 0.575267i
\(711\) 0 0
\(712\) 14.4497 + 12.1247i 0.541526 + 0.454394i
\(713\) 0.189493 + 3.25347i 0.00709657 + 0.121843i
\(714\) 0 0
\(715\) −6.55882 8.81003i −0.245286 0.329476i
\(716\) 0.917404 0.107229i 0.0342850 0.00400734i
\(717\) 0 0
\(718\) −20.2571 + 13.3233i −0.755990 + 0.497222i
\(719\) 43.1137 15.6921i 1.60787 0.585216i 0.626852 0.779139i \(-0.284343\pi\)
0.981017 + 0.193922i \(0.0621209\pi\)
\(720\) 0 0
\(721\) −4.07379 1.48274i −0.151716 0.0552200i
\(722\) −6.28670 + 1.48997i −0.233967 + 0.0554511i
\(723\) 0 0
\(724\) −0.0456669 + 0.784070i −0.00169720 + 0.0291397i
\(725\) −7.98355 + 8.46207i −0.296502 + 0.314273i
\(726\) 0 0
\(727\) 6.39466 + 14.8245i 0.237165 + 0.549810i 0.994681 0.103007i \(-0.0328464\pi\)
−0.757516 + 0.652817i \(0.773587\pi\)
\(728\) 8.56403 0.317404
\(729\) 0 0
\(730\) −27.6992 −1.02519
\(731\) 18.3372 + 42.5105i 0.678227 + 1.57231i
\(732\) 0 0
\(733\) 17.6698 18.7289i 0.652648 0.691767i −0.313549 0.949572i \(-0.601518\pi\)
0.966197 + 0.257805i \(0.0829993\pi\)
\(734\) 1.13663 19.5151i 0.0419536 0.720316i
\(735\) 0 0
\(736\) 0.756375 0.179264i 0.0278803 0.00660776i
\(737\) 50.7756 + 18.4808i 1.87034 + 0.680750i
\(738\) 0 0
\(739\) −16.9934 + 6.18508i −0.625111 + 0.227522i −0.635102 0.772428i \(-0.719042\pi\)
0.00999089 + 0.999950i \(0.496820\pi\)
\(740\) 3.30334 2.17264i 0.121433 0.0798678i
\(741\) 0 0
\(742\) 13.9239 1.62747i 0.511162 0.0597463i
\(743\) −26.4761 35.5636i −0.971314 1.30470i −0.952391 0.304880i \(-0.901384\pi\)
−0.0189230 0.999821i \(-0.506024\pi\)
\(744\) 0 0
\(745\) −0.687201 11.7988i −0.0251771 0.432274i
\(746\) −0.247642 0.207797i −0.00906683 0.00760798i
\(747\) 0 0
\(748\) 3.46379 2.90646i 0.126649 0.106271i
\(749\) −5.78095 6.12744i −0.211231 0.223892i
\(750\) 0 0
\(751\) −2.09320 1.37672i −0.0763819 0.0502372i 0.510744 0.859733i \(-0.329370\pi\)
−0.587126 + 0.809496i \(0.699741\pi\)
\(752\) 0.857459 + 0.203222i 0.0312683 + 0.00741073i
\(753\) 0 0
\(754\) 11.9330 + 1.39477i 0.434575 + 0.0507946i
\(755\) 2.14057 + 3.70758i 0.0779034 + 0.134933i
\(756\) 0 0
\(757\) 21.8769 37.8919i 0.795129 1.37720i −0.127629 0.991822i \(-0.540737\pi\)
0.922757 0.385381i \(-0.125930\pi\)
\(758\) 21.4515 28.8144i 0.779155 1.04659i
\(759\) 0 0
\(760\) −5.91942 19.7722i −0.214720 0.717215i
\(761\) 41.2979 20.7406i 1.49705 0.751846i 0.503366 0.864073i \(-0.332095\pi\)
0.993683 + 0.112227i \(0.0357984\pi\)
\(762\) 0 0
\(763\) 10.0564 33.5908i 0.364067 1.21607i
\(764\) −0.658078 3.73214i −0.0238084 0.135024i
\(765\) 0 0
\(766\) 2.18168 12.3729i 0.0788272 0.447051i
\(767\) 2.86531 + 1.43901i 0.103460 + 0.0519598i
\(768\) 0 0
\(769\) 11.5490 26.7737i 0.416469 0.965483i −0.572843 0.819665i \(-0.694159\pi\)
0.989311 0.145818i \(-0.0465814\pi\)
\(770\) 7.27165 16.8576i 0.262052 0.607505i
\(771\) 0 0
\(772\) −3.02306 1.51824i −0.108802 0.0546427i
\(773\) −6.90323 + 39.1502i −0.248292 + 1.40813i 0.564429 + 0.825481i \(0.309096\pi\)
−0.812721 + 0.582653i \(0.802015\pi\)
\(774\) 0 0
\(775\) 2.05395 + 11.6485i 0.0737801 + 0.418427i
\(776\) 1.02260 3.41574i 0.0367094 0.122618i
\(777\) 0 0
\(778\) 33.3343 16.7411i 1.19509 0.600198i
\(779\) 14.0177 + 46.8225i 0.502238 + 1.67759i
\(780\) 0 0
\(781\) −24.2513 + 32.5751i −0.867779 + 1.16563i